Fourier Collocation and Reduced Basis Methods for Fast Modeling of Compressible Flows (Communications in Computational Physics, 2022)
A projection-based reduced order model (ROM) based on the Fourier collocation method is proposed for compressible flows. The incorporation of localizedartificial viscosity model and filtering is pursued to enhance the robustness and accuracy of the ROM for shock-dominated flows. Furthermore, for Euler systems, ROMsbuilt on the conservative and the skew-symmetric forms of the governing equation arecompared. To ensure efficiency, the discrete empirical interpolation method (DEIM)is employed. An alternative reduction approach, exploring the sparsity of viscosityis also investigated for the viscous terms. A number of one- and two-dimensionalbenchmark cases are considered to test the performance of the proposed models. Results show that stable computations for shock-dominated cases can be achieved withROMs built on both the conservative and the skew-symmetric forms without additional stabilization components other than the viscosity model and filtering. Underthe same parameters, the skew-symmetric form shows better robustness and accuracythan its conservative counterpart, while the conservative form is superior in terms ofefficiency.
Keywords: Projection-based reduced order modeling; Fourier collocation; artificial viscosity; compressible flow.